一种用于压缩感知理论的投影矩阵优化算法.pdf

第37 卷第7 期 电 子 与 信 息 学 报 Vol.37 No.7 2015 年7 月 Journal of Electronics Information Technology Jul. 2015 一种用于压缩感知理论的投影矩阵优化算法 吴光文*①② 张爱军① 王昌明① ①(南京理工大学机械工程学院 南京 210094) ②(东华理工大学电子与机械工程学院 抚州 344000) 摘 要：考虑到投影矩阵对压缩感知(CS)算法性能的影响，该文提出一种优化投影矩阵的算法。该方法提出可导 的阈值函数，通过收缩 Gram 矩阵非对角元的方法压缩投影矩阵和稀疏字典的相关系数，引入基于沃尔夫条件 (Wolfe’s conditions)的梯度下降法求解最佳投影矩阵，达到提高投影矩阵优化算法稳定度和重构信号精度的目的。 通过基追踪(BP)算法和正交匹配追踪(OMP)算法求解l0 优化问题，用压缩感知方法实现随机稀疏向量、小波测试 信号和图像信号的感知和重构。仿真实验表明，该文提出的投影矩阵优化算法能较大地提高重构信号的精度。 关键词：压缩感知；相干性；基追踪算法；正交匹配追踪算法 中图分类号：TN911.7 文献标识码： A 文章编号：1009-5896(2015)07-1681-07 DOI: 10.11999/JEIT141450 Novel Optimization Method for Projection Matrix in Compress Sensing Theory Wu Guang-wen①② Zhang Ai-jun① Wang Chang-ming① ① (School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China) ②(Department of Electronic Engineering, East China Institute of Technology, Fuzhou 344000, China) Abstract: Considering the influence of the projection matrix on Compressed Censing (CS), a novel method is proposed to optimize the projection matrix. In order to improve the signal’s reconstruction precise and the stability of the optimization algorithm of the projection matrix, the proposed method adopts a differentiable threshold function to shrink the off-diagonal items of a Gram matrix corresponding to the mutual coherence between the projection matrix and sparse dictionary, and introduces a gradient descent approach based on the Wolf ’s-conditions to solve the optimization projection matrix. The Basis-Pursuit (BP) algorithm and the Orthogon